# a) Let E be a nonempty subset of X. Prove that a is a cluster point of E if and only if for each r > 0, E Br(a) (a) is nonempty. b) Prove that every bounded infinite subset of R has at least one cluster point.

a) Let E be a nonempty subset of X. Prove that a is a cluster point of E if and only if for each r > 0, E ∩ Br(a) \ (a) is nonempty.

b) Prove that every bounded infinite subset of R has at least one cluster point.

b) Prove that every bounded infinite subset of R has at least one cluster point.

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